Possible to combine a pie.operator and box.operator together?
No, you cannot have all 8 pie positions and another extra box.

You can have boxes instead some pie positions though. So you can have 7 pie positions and the bottom 8th one being a box:

def draw(self, context):
    layout = self.layout
    pie = layout.menu_pie()
    #4 - LEFT
    pie.operator("mesh.primitive_cube_add", text="LEFT", icon='MESH_CUBE')
    #6 - RIGHT
    pie.operator("mesh.primitive_cube_add", text="RIGHT", icon='MESH_CUBE')
    #2 - BOTTOM
    box = pie.box().column()
    box.operator("mesh.primitive_cube_add", text="BOTTOM 1", icon='MESH_CUBE')
    box.operator("mesh.primitive_cube_add", text="BOTTOM 2", icon='MESH_CUBE')
    box.operator("mesh.primitive_cube_add", text="BOTTOM 3", icon='MESH_CUBE')
    box.operator("mesh.primitive_cube_add", text="BOTTOM 4", icon='MESH_CUBE')
    #8 - TOP
    pie.operator("mesh.primitive_cube_add", text="TOP", icon='MESH_CUBE')
    #7 - TOP - LEFT
    pie.operator("mesh.primitive_cube_add", text="TOP - LEFT", icon='MESH_CUBE')
    #9 - TOP - RIGHT
    pie.operator("mesh.primitive_cube_add", text="TOP - RIGHT", icon='MESH_CUBE')
    #1 - BOTTOM - LEFT
    pie.operator("mesh.primitive_cube_add", text="BOTTOM - LEFT", icon='MESH_CUBE')
    #3 - BOTTOM - RIGHT
    pie.operator("mesh.primitive_cube_add", text="BOTTOM - RIGHT", icon='MESH_CUBE')


You can split rows, create multiple columns, etc. Normal formatting methods of Blender UI applies. If you omit the .box() you don't have that ugly border and only grouped entries which looks better imho.